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Mechanical Properties of Fluids

Applications of Bernoulli's Theorem

A uniform cylindrical block of length l density d_{1} and area

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Solving time: 3 mins

A uniform cylindrical block of length $l$ density $d_{1}$ and area of cross section $A$ floats in a liquid of density $d_{2}$ contained in a vessel $(d_{2} > d_{1})$ . The bottom of the cylinder just rests on a spring of constant $k$ . The other end of the spring is fixed to the bottom of the vessel. A weight that may be placed on top of the cylinder such that the cylinder is just submerged in the liquid. Find the weight.

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Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

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Eleanor Discussed

A uniform cylindrical block of length

l

density

d_{1}

and area of cross section

A

floats in a liquid of density

d_{2}

contained in a vessel

(d_{2} > d_{1})

. The bottom of the cylinder just rests on a spring of constant

k

. The other end of the spring is fixed to the bottom of the vessel. A weight that may be placed on top of the cylinder such that the cylinder is just submerged in the liquid. Find the weight.

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

A \times l \times d_{1} \times g l d_{1} x d_{2} x w + w_{b} w = A \times (l - x) \times d_{2} \times g = l d_{2} - x d_{2} = l (d_{2} - d_{1}) = l (1 - \frac{d _{1}}{d _{2}}) = k x + F_{u} = F_{u} + k x - w_{b}

W = A \times l \times d_{2} \times g + k l [1 - \frac{d _{1}}{d _{2}}) - A \times l \times d_{1} \times g

W = A l g (d_{2} - d_{1}) + k l \frac{( d _{2} - d _{1} )}{d _{2}}

W = (d_{2} - d_{1}) (A l g + \frac{k l}{d _{2}})

W = [l (d_{2} - d_{1}) (\frac{k}{d _{2}} + A g)]

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Question Text	A uniform cylindrical block of length $l$ density $d_{1}$ and area of cross section $A$ floats in a liquid of density $d_{2}$ contained in a vessel $(d_{2} > d_{1})$ . The bottom of the cylinder just rests on a spring of constant $k$ . The other end of the spring is fixed to the bottom of the vessel. A weight that may be placed on top of the cylinder such that the cylinder is just submerged in the liquid. Find the weight.
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	82

Text solutionVerified

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